Can we expect support for running Unreal engine games inside Flutter applications like Unity does?

Unity apparently has support for running inside Flutter developed apps:

Can we expect similar support with Unreal Engine 4 in the future?

Definately just as Unity offers standalone package that could be added to Android Project similarly UE4 will also offer this in few updates.
The work is in progress as far as Flutter is conderend since Flutter is Cross Platform so does UNREAL so their is chance that UNREAL will someday support flutter but i don;t think hat they will see this as priority for Mobile platform right now.
Flutter as provide better UX which is key to good games I too hope that this is added to UNREAL as soon as it could.

Would be great if a staff member can confirm this…

I am not Unreal Staff but pretty sure that flutter for UE4 will not available for couple of Years.